Digital Commons Network^™

David Tall And Advanced Mathematical Thinking, Keith Weber

The Mathematics Enthusiast

I discuss David Tall’s influence on advanced mathematical thinking.

Part 4: Epilogue, Corey Brady, Luis Moreno-Armella

The Mathematics Enthusiast

In closing our set of of articles, we reflect back on the nature of mathematical thinking and learning with representations, especially the computational, executable representations that are enabled by modern dynamic mathematics environments. These aspects of the development of mathematical ideas have profound implications for our approaches to the teaching and learning of Calculus. Our narrative approach has dramatized the radically fruitful and generative nature of the period during which the ideas of Calculus were stabilized (especially in the stories of Guillermo/Leibniz and Leonardo/Euler). An analogy between the development of the field and the development of individual learners, should caution …

Recollections Of Simon, Chris Rasmussen

The Mathematics Enthusiast

Chris Rasmussen’s tribute to Simon Goodchild.

Rational Approximations Of Sine And Cosine, Mashrur Azim, Christopher Griffin

The Mathematics Enthusiast

In this paper, we use elementary methods to derive a rational function over the integers to approximate the trigonometric sine function on the interval [0, π/2]. This formula can then be used to derive a quartic polynomial with a root close to π/3 , providing an interesting algebraic approximation to this value. A more accurate rational function over the reals is then computed using numerical optimization. This new formula, while more accurate, provides a worse approximation of π/3 in the corresponding quartic equation, showing the trade-offs in local vs. global approximation. This paper is accessible to undergraduates and illustrates a …

Rethinking Equality In Mathematics Education With Category Theory, Kelly Paton

The Mathematics Enthusiast

To provide an alternative to the flattening operations of equality, which are prevalent not only in mathematics but also in our everyday world, I introduce the relational structures of category theory and their more nuanced notions of equivalence. Instead of defaulting to a binary assignation of equal or not-equal, equivalence posits that contextual relationships are integral to how we conceive of ‘same’ and ‘different’. I draw upon the ideas of philosophers who work against the erasure of diversity and offer ways to uphold difference while searching for commonalities. As I trace the sociopolitical implications of embracing an ontological framework built …

Wonders Of Multiplication Table, Amir H. Asghari

The Mathematics Enthusiast

This paper originated as a talk for school teachers, aimed at demonstrating that the multiplication table is more than a simple memory aid. Instead, it is a powerful tool for exploring mathematical patterns and plays an essential role in both the discovery and teaching of mathematics. The initial goal was to illustrate how the table could act as a bridge between arithmetic, algebra, and proof. However, as the author delved into the table, its intricate structure began to unfold, with each idea seamlessly leading to the next. This evolution transformed the table’s utility far beyond its initial educational purpose. This …

Analysis Of The Status And Thematic Trends Of Ai For Science Research Abroad From 2015 To 2024, Fangyuan Wang, Huiting Xu, Jinghua Xue

Journal of Scientific Information Research

[Purpose/significance] This paper analyzes the relevant literature in the field of AI for Science（AI4S）in the WoS core database from 2015 to 2024, and sorts out the research status and development trends in this field, aiming to provide forward-looking insights for the application of AI technology in scientific research.

[Method/process] This paper combines bibliometric analysis with the BERTopic model to analyze the publication trends, publishing countries, core authors, and topic identification and development trends in the field of AI4S.

[Result/conclusion] Through bibliometric analysis, this paper reveals the exponential growth trend of AI4S-related literature, and finds that China ranks first in the …

Construction Of China's Online Platform Information Value Evaluation System, Shuyue Fang, Yuan Sun, Yuwei Ye, Liling Xia

Journal of Scientific Information Research

[Purpose/significance] This paper aims to explore the construction of the information value evaluation system of online platforms in China, so as to provide theoretical support and practical guidance for the information management of online platforms.

[Method/process] This paper firstly explores the connotation and dimension of the information value of the online platforms, and uses the analytic hierarchy process to distribute the weight, then,obtains the comprehensive evaluation results of the information value of each online platform through the fuzzy comprehensive evaluation method.

[Result/discussion] Through the comprehensive evaluation of the information interaction platforms, the multilateral trading platforms and the complementary innovation platform, …

Threading Hmong Culture Into Math: Supporting Hmong Elementary Students Through Integrative Practices, Lisa Vang

School of Education and Leadership Student Capstone Projects

The research question answered in this capstone paper is: “How can educators integrate Hmong culture into their math instruction in ways that support both academic growth and cultural identity?” This paper focuses on the need for culturally responsive teaching in mathematics for elementary Hmong students and the convergence of cultural identity, student engagement, and meaningful learning experiences. This capstone paper includes a literature review that explores culturally responsive pedagogies and practices in classrooms, the importance of cultivating mathematical identity in Hmong students, and the integration of Hmong culture into elementary math instruction. The results of this capstone paper lead to …

Utilizing Best Practices In The Classroom In Regards To Technology Use, Kathryn Robinson

School of Education and Leadership Student Capstone Projects

The research question addressed in this capstone project is: “In what ways do best practices in technology use in the classroom support teachers and students?” During the COVID-19 pandemic, schools were forced to shift online to protect student health. As schools have returned to in-person learning, the influx of technology has not decreased. Studies show that technology use, whether it be social media, screen time, TV, or videogames can be detrimental to brain development. Because of this, it is crucial that there are guidelines for best practice when using technology in the classroom. Further, healthy habits surrounding technology use outside …

The Role Of Gamified Learning In Developing Math Confidence And Procedural Fluency, Celeste Nosow

School of Education and Leadership Student Capstone Projects

This capstone project sought to answer: In what ways might a gamified math fluency resource focused on increasing math confidence facilitate learning for preadolescent students struggling in math? Research into game-based learning, motivation, and mindset revealed that students can benefit from engaging, collaborative, and low-stakes learning experiences that build fluency through games. Additionally, the environment should foster math confidence and competence in preadolescent learners. The project culminated in the development of a website offering free, low-preparation math games appropriate for grades 3–5. Designed for teachers and substitute educators, the learning materials provided emphasize social interaction, inclusivity, and equitable access. This …

Outdoor Trail Use At Woodland Elementary School For Student Engagement With Mn Life Science Standards, Barbara Walswick

School of Education and Leadership Student Capstone Projects

This paper examines use of the unpaved trails at Woodland Elementary School for student engagement with the third grade MN life science curriculum standards. At this time, the nature resource behind the school is underused. Research on benefits of outdoor learning for elementary students and staff was conducted and noted, resulting in the Woodland Trail Guide project. It serves as a life science curriculum companion for educators to easily take their students on the trails for increased student engagement. It gives educators experience and confidence to optimize the trails in teaching their science lessons and serves as a catalyst to …

College Of Natural Sciences Newsletter, Fall 2025, College Of Natural Sciences

College of Natural Sciences Newsletters and Reports

P.1 Dean's Message from Dr. Sen Subramanian
P.2 Student Spotlights
P.3 One Day for STATE
P.4 Fun Filming with Jack
P.5 Germanium Studies
P.6 Research Expenditures
P.8 Increased Enrollment
P.9 Faculty Recognition
P.11 Scoops & Smiles

Examining The City Of Philadelphia’S Proposition Bill #250768 “Stop Trashing Our Air Act” By Addressing Waste Management And Environmental Justice Challenges In Chester City, Pennsylvania And The Philadelphia Region, Dylan Wascavage

Student Publications

This paper offers a policy analysis of the City of Philadelphia’s "Stop Trashing Our Air Act" by summarizing the reasoning for the bill's call to action, its legislative background, identifying key players and their strategies, and how these strategies reflect philosophies of environmental governance and the policy cycle. It seeks to inform local community members and policymakers of the implications of this bill, to highlight the lack of state and federal intervention on this issue, and to address the environmental justice and pollution concerns of the Covanta waste incinerator in Chester City and its neighboring communities. It also aims to …

Trust And Ethics In Ai-Driven E-Commerce: Persuasion Vs. Privacy, Akriti Nepal

Student Publications

This study examines how AI-driven features in e-commerce influence user satisfaction and the role of trust in these interactions. Using a survey-based dataset of 100 consumers, we investigated whether trust moderates or mediates the impact of AI persuasiveness and perceptions of bias, intrusiveness, and preference understanding on satisfaction. Results indicate that AI’s perceived ability to understand user preferences strongly predicts satisfaction, while trust partially mediates the relationship between helpful AI features and urgency messages and user satisfaction. Conversely, trust did not significantly moderate these relationships, and concerns about bias and intrusiveness had minimal impact. Findings suggest that AI-driven satisfaction is …

A Call For Canceling Compassionate Release And Restoring Federal Parole, Honorable Chief Judge C.J. Williams

Washington and Lee Law Review

The current federal sentencing scheme is a patchwork quilt of provisions that grant judges virtually unfettered and unreviewable discretion imposing sentences on the front-end and in granting compassionate release on the back end. It was not designed in the beginning to be this way. The advisory-only sentencing guidelines scheme we have now resulted from the Supreme Court’s finding that mandatory guidelines violated the Constitution. The recent sentencing reform movement—of which compassionate release is a significant part—has sought to find ways of ameliorating what is seen as the draconian result of the war on drugs. The question is whether granting Article …

Iowa Waste Reduction Center Newsletter, October 2025, University Of Northern Iowa. Iowa Waste Reduction Center.

Iowa Waste Reduction Center Newsletter

Contents:

--- Joe Bolick named NPPR Chair
--- Open House Party Recap
--- Green Brewery Certification has come to Missouri
--- Clear guidance, real results: IAEAP
--- AI training for Waste Partners

(Si15-084) Application Of Differentiation Matrices Corresponding To Scaling And Wavelet Functions To Integral Equations, Viresh Kumar, Rakesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, we have studied the technique by which a differentiation matrix corresponding to scaling and wavelet function is helpful in representing an integral equation in discrete form. In this technique, only finite times continuously differentiable scaling and wavelet functions were used for the differentiation matrix. This method explores the applications of compactly supported wavelets in discretization of Fredholm integral equation and provides us with a bridge for the solution of integral equations via compactly supported finitely differentiable wavelets.

(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms, M. Kapoor, B. K. Pathak, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Construction projects are influenced by various uncertain factors, including supervisory knowledge, labor expertise, and weather conditions. These uncertain factors have linguistic properties that are challenging to quantify with the help of traditional set theory. To address this, the study applies fuzzy inference systems, specifically the Mamdani fuzzy inference system, to model and evaluate the impact of these uncertainties on construction projects. This fuzzy inference system provides a more nuanced understanding of these factors compared to traditional set theory methods. Experimental results indicate that uncertainties significantly impact construction projects. These findings establish a valuable framework for developing adaptive strategies, enhancing project …

(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution, Priyadharshini R., Shalini K., Hemalatha R., Sangeetha S.

Applications and Applied Mathematics: An International Journal (AAM)

The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use …

(Si15-142) Selection Of Single Sampling Plans Based On Zero Inflated Binomial Distribution Using Cost Optimization, Sangeetha S., Shalini K., Hemalatha R., Priyadharshini R.

Applications and Applied Mathematics: An International Journal (AAM)

Economic design of sampling plans involves creating sampling plans that minimize the total cost associated with the inspection process while ensuring quality. It aims to address the quality risk concerns of both producer and consumer, ensuring product quality while minimizing inspection costs. This article’s objective is to design single sampling plans by attributes based on Zero-inflated Binomial (ZIB) distribution, using cost optimization principles by developing an economic model aimed at achieving optimal total cost by considering the Average Total Inspection (ATI). Numerical illustration is provided to illustrate the selection of single sampling plans under ZIB distribution that minimizes producer’s total …

(Si15-093) Dynamics Of The Generalized Nonlinear Schrödinger Equation With A Source Using An Analytical Method, Manish Raghav, Manoj .

Applications and Applied Mathematics: An International Journal (AAM)

In the present article, an analytical method is used to obtain hyperbolic, trigonometric, and rational solutions of the generalized nonlinear Schrödinger (GNLS) equation with a source. The ability of solitons to preserve their shapes during propagation makes them suitable for optical fiber communication. Solutions to the generalized nonlinear Schrödinger equation with a source can also describe solitons, and understanding their dynamics helps to design communication systems based on solitons. The analytical method used is compelling and effective for finding exact solutions to various nonlinear evolution equations (NLEEs). To further understand the phenomena, we create 3−D, contour, and 2−D graphs of …

(Si15-113) Augmenting Cryptographic Security Through Inventive Application Of The Kharrat-Toma Transform Algorithm, Prabakaran Raghavendran, Tharmalingam Gunasekar, K. Sakthivel, Kamalendra Kumar, Shalini Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper introduces a cryptographic technique combining the Kharrat-Toma Transform and congruence modulo operators to improve the security of message encryption. The proposed model uses the mathematical properties of the Kharrat-Toma Transform and its inverse for direct scrambling and unscrambling processes while embedding sufficient complexity to resist modern cryptanalytic attacks. The model is subjected to experimental tests, including encryption quality analysis, Shannon entropy, and NIST randomness tests, in order to prove the strength of the model. Through encryption quality analysis, symbol frequencies in the ciphertext are masked heavily from having much correlation between plaintext and ciphertext. Entropy values indicate near-theoretical …

(Si15-107) Mathematical Modeling Of Cancer Dynamics Stability Analysis Of Post Therapy Protection, Rajendran Swetha, Tharmalingam Gunasekar, Kamalendra Kumar, Krishnasamy Sakthivel

Applications and Applied Mathematics: An International Journal (AAM)

The study of PSITPS mathematical model is developed to analyze cancer dynamics, focusing on post-therapy protection. The model’s solution is rigorously examined for boundedness and positivity of solutions. Equilibrium points are identified, and numerical methods are employed to study stability. Simulations using accurate cancer data demonstrate the effectiveness of post-treatment protection in controlling cancer spread and minimizing recurrence. Stability analysis confirms the model’s predictive capability, offering valuable insights into long-term patient outcomes. The results highlight the importance of continuous post-treatment care in improving survival rates and reducing disease prevalence. This study provides a framework for optimizing cancer treatment strategies by …

(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets, S. Anita Shanthi, R. Preethi

Applications and Applied Mathematics: An International Journal (AAM)

Decision making, in the present contemporary world, has been inherently complicated. Nowadays, the major challenge is the selection of an appropriate option. The arrival of numerous brands and models makes a purchase challenging. Hence, in this paper, four different models of the same branded laptops are considered, for the selection of an appropriate option, using the Analytic Hierarchy Process (AHP) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), with bipolar fuzzy sets, which help decision makers arrive at the most logical choice based on their preferences. The bipolar fuzzy Analytic Hierarchy Process efficaciously supports decision making in cases …

Ethical Considerations, Determinations, And Suggestions For Implementation Of Generative Artificial Intelligence In The Classroom, Becky Molin

School of Education and Leadership Student Capstone Projects

The research question addressed in this capstone project is: “How can students and educators ethically use Generative AI in the classroom?” This paper, created for the benefit of general education classroom staff, details the creation of a professional development intended to inform educators about the pros, cons, and possible implementations of Generative AI in secondary and tertiary classrooms. The six key topics covered in the capstone are: Defining Generative AI, Ethics of Generative AI, The Effects of Generative AI on the Human Brain, Perception of Generative AI in Education, and finally Monitoring, Teaching About & Handling Generative AI in Schools. …

Wooster Magazine: Annual Report Edition 2024-25, Caitlin Paynich Stanowick

Wooster Magazine: 2021-2030

The fall Annual Report Edition 2024-25 of Wooster magazine highlights a year of meaningful progress and shared achievement across campus. The annual financial review reports on the College’s operating revenues and expenses and showcases the ways donors contributed to the ongoing success of Wooster and its students in the past year. New endowments honoring beloved professors Ralph Bangham of biology and Nancy Ditmer of music are highlighted. Members of the Class of 2025 share their new paths in graduate study, research, and fulfilling careers. Wooster’s new minors in climate studies and humanities, arts and creative computing broaden curricular opportunities, providing …

Mentoring And Entrepreneurship In Higher Education: A Study From The Plithogenic Statistics, Wilmer Ortega Chávez, Janett Karina Vásquez Pérez, Beker Maraza Vilcanqui, Nazario Aguirre Baique, Carlos Manuel Sacarías Mercado, Ciro Angel Lazo Salcedo, Reyna Olano Del Castillo

Neutrosophic Sets and Systems

Entrepreneurship management in university students is a key factor for economic and social development, especially in intercultural contexts such as the Peruvian Amazon. However, the absence of effective training strategies limits the strengthening of these competencies. This study aims to evaluate the impact of a mentoring program on strengthening entrepreneurship management in students at the National Intercultural University of the Amazon in Peru. The research concludes that the implementation of mentoring programs can represent a key strategy to promote student entrepreneurship in regions with development needs, providing relevant evidence for educational practice and future interventions in higher education. Plithogenic statistics …

Predictive Modeling Of Atrial Fibrillation Using A Hybrid Multinomial-Neutrosophic Approach For Biomarker Identification, Lorenzo Cevallos-Torres, Luis Pilacuan-Bonete, Rosangela Caicedo-Quiroz, Franklin Parrales-Bravo, Eduardo Rubio-Bonito

Neutrosophic Sets and Systems

Atrial fibrillation, characterized by chaotic rhythms and electrical complexity, presents a diagnostic challenge that requires innovative approaches to uncover its underlying biomarkers. This study proposes a hybrid predictive model based on multinomial logistic regression and neutrosophic logic, aiming to identify clinically significant patterns associated with this condition. Using the Knowledge Discovery in Databases (KDD) methodology, large volumes of cardiovascular data are analyzed to distinguish meaningful signals from background noise, revealing hidden connections and validating medical hypotheses. The implementation of the model through a digital prototype reflects a convergence of advanced statistics, artificial intelligence, and cardiovascular medicine, promoting a multidisciplinary approach. …

(Si15-022) Five Efficient Cryptography Authentication Schemes With Functional Relation On General Spaces, L. Sreenivasulu Reddy, S. Lakshmisri

Applications and Applied Mathematics: An International Journal (AAM)

This work addresses the growing demand for diversification in cryptographic schemes to secure communication. This work proposes a novel suite of algorithms, including two block ciphers (TPBlock and TAP-Block), two stream ciphers (TP-Stream and TAP-Stream), and a zero-knowledge proof scheme (F-zero knowledge proof). All schemes leverage functional relations defined over the real number space with a dimension greater than one for encryption, decryption, and key generation, offering an alternative to the number-theoretical aspects and algebraic structures commonly used in existing schemes. The main goal of this work is to introduce and propose these five novel cryptographic schemes to provide authentication …